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Journal articles on the topic 'Invariance to external perturbations'

Author: Grafiati

Published: 30 May 2022

Last updated: 31 May 2022

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1

Shu, Hai, and Hongtu Zhu. "Sensitivity Analysis of Deep Neural Networks." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 4943–50. http://dx.doi.org/10.1609/aaai.v33i01.33014943.

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Deep neural networks (DNNs) have achieved superior performance in various prediction tasks, but can be very vulnerable to adversarial examples or perturbations. Therefore, it is crucial to measure the sensitivity of DNNs to various forms of perturbations in real applications. We introduce a novel perturbation manifold and its associated influence measure to quantify the effects of various perturbations on DNN classifiers. Such perturbations include various external and internal perturbations to input samples and network parameters. The proposed measure is motivated by information geometry and provides desirable invariance properties. We demonstrate that our influence measure is useful for four model building tasks: detecting potential ‘outliers’, analyzing the sensitivity of model architectures, comparing network sensitivity between training and test sets, and locating vulnerable areas. Experiments show reasonably good performance of the proposed measure for the popular DNN models ResNet50 and DenseNet121 on CIFAR10 and MNIST datasets.

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2

Bruhn, B., and B. P. Koch. "Heteroclinic Bifurcations and Invariant Manifolds in Rocking Block Dynamics." Zeitschrift für Naturforschung A 46, no. 6 (June 1, 1991): 481–90. http://dx.doi.org/10.1515/zna-1991-0603.

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Abstract A simple model of rigid block motion under the influence of external perturbations is discussed. For periodic forcings we prove the existence of Smale horseshoe chaos in the dynamics. For slender blocks a heteroclinic bifurcation condition is calculated exactly, i.e. without using perturbation methods. That means that our results are valid for arbitrary excitation amplitudes. Furthermore, analytical formulas for the first pieces of the stable and unstable manifolds are derived not only for periodically but also for transiently driven systems. In the case of small excitation and damping the Melnikov method is used to treat the full nonlinear problem

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Meng, Bo, Cun Chen Gao, and Shu Hong Tang. "Adaptive Variable Structure Control for Uncertain Linear Time-Invariant Delay Singular Systems." Advanced Materials Research 433-440 (January 2012): 3734–40. http://dx.doi.org/10.4028/www.scientific.net/amr.433-440.3734.

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This paper discusses the control problems of singular linear time-invariant delay systems with uncertainties. A new adaptive variable structure control strategy is given by Lyapunov stability theory. The invariance of sliding mode is proved in the circumstances of the external disturbance and parameter perturbation with matching conditions. Through memory and memoryless of the linear state feedback, the control strategy ensure that system reaches sliding mode in finite time and the closed-loop system is global asymptotic stable. Simulation results further show that the strategy is feasible and effective.

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PARESCHI, FABIO, RICCARDO ROVATTI, and GIANLUCA SETTI. "PERIODICITY AS CONDITION TO NOISE ROBUSTNESS FOR CHAOTIC MAPS WITH PIECEWISE CONSTANT INVARIANT DENSITY." International Journal of Bifurcation and Chaos 16, no. 11 (November 2006): 3391–400. http://dx.doi.org/10.1142/s0218127406016872.

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Chaotic maps represent an effective method of generating random-like sequences, that combines the benefits of relying on simple, causal models with good unpredictability. However, since chaotic maps behavior is generally strongly dependent on unavoidable implementation errors and external perturbations, the possibility of guaranteeing map statistical robustness is of great practical concern. Here we present a technique to guarantee the independence of the first-order statistics of external perturbations, modeled as an additive, map-independent random variable. The developed criterion applies to a quite general class of maps.

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Omrani, Mohsen, J. Andrew Pruszynski, Chantelle D. Murnaghan, and Stephen H. Scott. "Perturbation-evoked responses in primary motor cortex are modulated by behavioral context." Journal of Neurophysiology 112, no. 11 (December 1, 2014): 2985–3000. http://dx.doi.org/10.1152/jn.00270.2014.

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Corrective responses to external perturbations are sensitive to the behavioral task being performed. It is believed that primary motor cortex (M1) forms part of a transcortical pathway that contributes to this sensitivity. Previous work has identified two distinct phases in the perturbation response of M1 neurons, an initial response starting ∼20 ms after perturbation onset that does not depend on the intended motor action and a task-dependent response that begins ∼40 ms after perturbation onset. However, this invariant initial response may reflect ongoing postural control or a task-independent response to the perturbation. The present study tested these two possibilities by examining if being engaged in an ongoing postural task before perturbation onset modulated the initial perturbation response in M1. Specifically, mechanical perturbations were applied to the shoulder and/or elbow while the monkey maintained its hand at a central target or when it was watching a movie and not required to respond to the perturbation. As expected, corrective movements, muscle stretch responses, and M1 population activity in the late perturbation epoch were all significantly diminished in the movie task. Strikingly, initial perturbation responses (<40 ms postperturbation) remained the same across tasks, suggesting that the initial phase of M1 activity constitutes a task-independent response that is sensitive to the properties of the mechanical perturbation but not the goal of the ongoing motor task.

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Wexler, Mark, Marianne Duyck, and Pascal Mamassian. "Persistent states in vision break universality and time invariance." Proceedings of the National Academy of Sciences 112, no. 48 (November 16, 2015): 14990–95. http://dx.doi.org/10.1073/pnas.1508847112.

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Studies of perception usually emphasize processes that are largely universal across observers and—except for short-term fluctuations—stationary over time. Here we test the universality and stationarity assumptions with two families of ambiguous visual stimuli. Each stimulus can be perceived in two different ways, parameterized by two opposite directions from a continuous circular variable. A large-sample study showed that almost all observers have preferred directions or biases, with directions lying within 90 degrees of the bias direction nearly always perceived and opposite directions almost never perceived. The biases differ dramatically from one observer to the next, and although nearly every bias direction occurs in the population, the population distributions of the biases are nonuniform, featuring asymmetric peaks in the cardinal directions. The biases for the two families of stimuli are independent and have distinct population distributions. Following external perturbations and spontaneous fluctuations, the biases decay over tens of seconds toward their initial values. Persistent changes in the biases are found on time scales of several minutes to 1 hour. On scales of days to months, the biases undergo a variety of dynamical processes such as drifts, jumps, and oscillations. The global statistics of a majority of these long-term time series are well modeled as random walk processes. The measurable fluctuations of these hitherto unknown degrees of freedom show that the assumptions of universality and stationarity in perception may be unwarranted and that models of perception must include both directly observable variables as well as covert, persistent states.

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7

Meinshausen, Nicolai, Alain Hauser, Joris M. Mooij, Jonas Peters, Philip Versteeg, and Peter Bühlmann. "Methods for causal inference from gene perturbation experiments and validation." Proceedings of the National Academy of Sciences 113, no. 27 (July 5, 2016): 7361–68. http://dx.doi.org/10.1073/pnas.1510493113.

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Inferring causal effects from observational and interventional data is a highly desirable but ambitious goal. Many of the computational and statistical methods are plagued by fundamental identifiability issues, instability, and unreliable performance, especially for large-scale systems with many measured variables. We present software and provide some validation of a recently developed methodology based on an invariance principle, called invariant causal prediction (ICP). The ICP method quantifies confidence probabilities for inferring causal structures and thus leads to more reliable and confirmatory statements for causal relations and predictions of external intervention effects. We validate the ICP method and some other procedures using large-scale genome-wide gene perturbation experiments in Saccharomyces cerevisiae. The results suggest that prediction and prioritization of future experimental interventions, such as gene deletions, can be improved by using our statistical inference techniques.

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Lebedeva, Т. Т., N. V. Semenova, and T. I. Sergienko. "Stability by the vector criterion of a mixed integer optimization problem with quadratic criterial fun ctions." Reports of the National Academy of Sciences of Ukraine, no. 10 (October 2020): 15–21. http://dx.doi.org/10.15407/dopovidi2020.10.015.

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The article is devoted to the study of qualitative characteristics of different concepts of stability of vector problems of mixed-integer optimization, namely, to identifying the conditions under which the set of Pareto-optimal solutions of the problem possesses some property of invariance defined in advance in relation to the external influences on initial data of the problem. We investigate the questions of stability with respect to data perturbations in a vector criterion of mixed-integer optimization problem. The necessary and sufficient conditions of stability of three types for a problem of finding the solutions of the Pareto set are found. Such conditions guarantee that the small variations of initial data of vector criterion: 1) do not result in new Paretooptimal solutions, 2) save all Pareto-optimal solutions of the problem and can admit new solutions, 3) do not change the set of Pareto-optimal solutions of the initial problem.

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van der Kooij, Herman, and Erwin de Vlugt. "Postural Responses Evoked by Platform Pertubations Are Dominated by Continuous Feedback." Journal of Neurophysiology 98, no. 2 (August 2007): 730–43. http://dx.doi.org/10.1152/jn.00457.2006.

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Is human balance control dominated by time invariant continuous feedback mechanisms or do noncontinuous mechanisms play a significant role like intermittent control? The goal of this paper is to quantify how much of the postural responses evoked by pseudorandom external periodic perturbations can be explained by continuous time invariant feedback control. Nine healthy subjects participated in this study. Center of mass and ankle torque responses were elicited by periodic platform perturbations in forward-backward directions containing energy in the 0.06- to 4.5-Hz frequency band. Subjects had their eyes open (EO) or eyes closed (EC). Responses were decomposed into a periodic component and a remnant (stochastic) component using spectral analysis. It is concluded that periodic responses can explain most of the evoked responses, although the remnant power spectral densities (PSDs) were significant especially for slow responses (<0.2 Hz) and largest for EC. The found remnant PSD did depend on the sensory condition but not on the platform perturbation amplitude. The ratio of the body sway and ankle torque remnant PSD reflects the body dynamics. Both findings are consistent with the idea that estimation of body orientation is part of a continuous feedback loop and that (stochastic) estimation errors increase when one source of sensory information is removed. The findings are not consistent with the idea that discrete or discontinuous intermittent feedback mechanisms significantly shape postural responses.

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Vignoni, Alejandro, Fabricio Garelli, and Jesús Picó. "Sliding Mode Reference Coordination of Constrained Feedback Systems." Mathematical Problems in Engineering 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/764348.

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This paper addresses the problem of coordinating dynamical systems with possibly different dynamics (e.g., linear and nonlinear, different orders, constraints, etc.) to achieve some desired collective behavior under the constraints and capabilities of each system. To this end, we develop a new methodology based on reference conditioning techniques using geometric set invariance and sliding mode control: the sliding mode reference coordination (SMRCoord). The main idea is to coordinate the systems references. Starting from a general framework, we propose two approaches: a local one through direct interactions between the different systems by sharing and conditioning their own references and a global centralized one, where a central node makes decisions using information coming from the systems references. In particular, in this work we focus in implementation on multivariable systems like unmanned aerial vehicles (UAVs) and robustness to external perturbations. To show the applicability of the approach, the problem of coordinating UAVs with input constraints is addressed as a particular case of multivariable reference coordination with both global and local configuration.

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11

Zhang, Jiao Long, and Wei Zhang. "Adaptive Fuzzy Sliding Mode Control for Uncertain Inverted Pendulum System." Applied Mechanics and Materials 273 (January 2013): 683–88. http://dx.doi.org/10.4028/www.scientific.net/amm.273.683.

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Firstly, the mathematical model of inverted pendulum system is created. Taking into account the uncertainty of inverted pendulum system external disturbances, adaptive fuzzy sliding mode controller is proposed with sliding mode control (SMC) theory and fuzzy logic theory. This controller can weaken the impact of uncertainty through fuzzification of the switching gain, Owing to Fuzzy approximation of the inverted pendulum system equations for an inverted pendulum with unknown parameters, this system achieve the adaptive control and optimize the control action. Secondly, inverted pendulum system has the features which SMC can keep invariance to the external disturbance and parameter perturbation. Lyapunov function is used to prove the stability of the controller. Simulation results also show that this controller can ensure inverted pendulum system fast response and robustness in the SIMULINK conditions.

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12

Oprisan, Sorinel A. "All Phase Resetting Curves Are Bimodal, but Some Are More Bimodal Than Others." ISRN Computational Biology 2013 (December 12, 2013): 1–11. http://dx.doi.org/10.1155/2013/230571.

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Phase resetting curves (PRCs) are phenomenological and quantitative tools that tabulate the transient changes in the firing period of endogenous neural oscillators as a result of external stimuli, for example, presynaptic inputs. A brief current perturbation can produce either a delay (positive phase resetting) or an advance (negative phase resetting) of the subsequent spike, depending on the timing of the stimulus. We showed that any planar neural oscillator has two remarkable points, which we called neutral points, where brief current perturbations produce no phase resetting and where the PRC flips its sign. Since there are only two neutral points, all PRCs of planar neural oscillators are bimodal. The degree of bimodality of a PRC, that is, the ratio between the amplitudes of the delay and advance lobes of a PRC, can be smoothly adjusted when the bifurcation scenario leading to stable oscillatory behavior combines a saddle node of invariant circle (SNIC) and an Andronov-Hopf bifurcation (HB).

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13

L’VOV, A. I. "THEORETICAL ASPECTS OF THE POLARIZABILITY OF THE NUCLEON." International Journal of Modern Physics A 08, no. 30 (December 10, 1993): 5267–303. http://dx.doi.org/10.1142/s0217751x93002095.

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Two aspects of the nucleon electromagnetic polarizabilities, αN and βN, are discussed. The first one is the interrelation between static and Compton polarizabilities. Relativistically consistent treatment of the polarization effects based on effective Lagrangians results in the conclusion that the Compton polarizabilities, rather than the static ones, drive the energy shift of the nucleon in external fields. The cluster substructure of the static polarizabilities is shown to be crucial for consistent calculations of the polarizabilities. The second aspect concerns the dominant role of pion degrees of freedom in αN as seen through dispersion relations, chiral perturbation theory, and constituent models. The reported calculations of αN within soliton models are shown to be inconsistent with gauge invariance. The difficulties in explaining the observed large diamagnetic component of βN are emphasized.

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14

Santos, Willien O., and Andre M. C. Souza. "Phenomenology of noncommutative phase space via the anomalous Zeeman effect in hydrogen atom." International Journal of Modern Physics A 29, no. 31 (December 20, 2014): 1450177. http://dx.doi.org/10.1142/s0217751x14501772.

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The Hamiltonian describing the anomalous Zeeman effect for the hydrogen atom on noncommutative (NC) phase space is studied using the nonrelativistic limit of the Dirac equation. To preserve gauge invariance, space noncommutativity must be dropped. By using first-order perturbation theory, the correction to the energy is calculated for the case of a weak external magnetic field. We also obtained the orbital and spin g-factors on the NC phase space. We show that the experimental value for the spin g-factor puts an upper bound on the magnitude of the momentum NC parameter of the order of [Formula: see text], 34 μ eV /c. On the other hand, the experimental value for the spin g-factor was used to establish a correction introduced by NC phase space to the presently accepted value of Planck's constant with an uncertainty of 2 part in 1035.

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15

Shmuelof, Lior, John W. Krakauer, and Pietro Mazzoni. "How is a motor skill learned? Change and invariance at the levels of task success and trajectory control." Journal of Neurophysiology 108, no. 2 (July 15, 2012): 578–94. http://dx.doi.org/10.1152/jn.00856.2011.

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The public pays large sums of money to watch skilled motor performance. Notably, however, in recent decades motor skill learning (performance improvement beyond baseline levels) has received less experimental attention than motor adaptation (return to baseline performance in the setting of an external perturbation). Motor skill can be assessed at the levels of task success and movement quality, but the link between these levels remains poorly understood. We devised a motor skill task that required visually guided curved movements of the wrist without a perturbation, and we defined skill learning at the task level as a change in the speed–accuracy trade-off function (SAF). Practice in restricted speed ranges led to a global shift of the SAF. We asked how the SAF shift maps onto changes in trajectory kinematics, to establish a link between task-level performance and fine motor control. Although there were small changes in mean trajectory, improved performance largely consisted of reduction in trial-to-trial variability and increase in movement smoothness. We found evidence for improved feedback control, which could explain the reduction in variability but does not preclude other explanations such as an increased signal-to-noise ratio in cortical representations. Interestingly, submovement structure remained learning invariant. The global generalization of the SAF across a wide range of difficulty suggests that skill for this task is represented in a temporally scalable network. We propose that motor skill acquisition can be characterized as a slow reduction in movement variability, which is distinct from faster model-based learning that reduces systematic error in adaptation paradigms.

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16

Sato, Yasuomi D., and Kazuyuki Aihara. "Changes of Firing Rate Induced by Changes of Phase Response Curve in Bifurcation Transitions." Neural Computation 26, no. 11 (November 2014): 2395–418. http://dx.doi.org/10.1162/neco_a_00653.

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We study dynamical mechanisms responsible for changes of the firing rate during four different bifurcation transitions in the two-dimensional Hindmarsh-Rose (2DHR) neuron model: the saddle node on an invariant circle (SNIC) bifurcation to the supercritical Andronov-Hopf (AH) one, the SNIC bifurcation to the saddle-separatrix loop (SSL) one, the AH bifurcation to the subcritical AH (SAH) one, and the SSL bifurcation to the AH one. For this purpose, we study slopes of the firing rate curve with respect to not only an external input current but also temperature that can be interpreted as a timescale in the 2DHR neuron model. These slopes are mathematically formulated with phase response curves (PRCs), expanding the firing rate with perturbations of the temperature and external input current on the one-dimensional space of the phase [Formula: see text] in the 2DHR oscillator. By analyzing the two different slopes of the firing rate curve with respect to the temperature and external input current, we find that during changes of the firing rate in all of the bifurcation transitions, the calculated slope with respect to the temperature also changes. This is largely dependent on changes in the PRC size that is also related to the slope with respect to the external input current. Furthermore, we find phase transition–like switches of the firing rate with a possible increase of the temperature during the SSL-to-AH bifurcation transition.

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17

Liu, Hao, Jianxiang Xi, and Yisheng Zhong. "Robust optimal attitude control of a laboratory helicopter without angular velocity feedback." Robotica 33, no. 2 (February 28, 2014): 282–94. http://dx.doi.org/10.1017/s0263574714000319.

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SUMMARYIn this paper, the robust, optimal, output control problem is dealt with for a 3-degree-of-freedom laboratory helicopter. The control goal is to achieve the practical tracking of the desired elevation and pitch angles without the angular velocity feedback. A nominal linear time-invariant system is introduced and the real system is considered as the nominal one with uncertainties, including parameter perturbations, nonlinear time-varying uncertainties, and external disturbances. An observer is first used to estimate angular velocity. Then a nominal controller based on the optimal control method is designed for the nominal system to achieve the desired tracking properties. Lastly, a robust output compensator is added to restrain the effects of uncertainties in the real system. It is shown that asymptotic tracking properties and robust stability can be achieved. Experimental results on the laboratory helicopter are shown to verify the effectiveness of the proposed control method.

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18

Gama, S., M. Vergassola, and U. Frisch. "Negative eddy viscosity in isotropically forced two-dimensional flow: linear and nonlinear dynamics." Journal of Fluid Mechanics 260 (February 10, 1994): 95–126. http://dx.doi.org/10.1017/s0022112094003459.

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The existence of two-dimensional flows with an isotropic and negative eddy viscosity is demonstrated. Such flows, when subject to a very weak large-scale perturbation of wavenumberkwill amplify it with a rate proportional tok2, independent of the direction.Specifically, it is assumed that the basic (unperturbed) flow is space-time periodic, possesses a centre of symmetry (parity-invariance) and has three- or six-fold rotational invariance to ensure isotropy of the eddy-viscosity tensor.The eddy viscosities emerging from the multiscale analysis are calculated by two different methods. First, there is an expansion in powers of the Reynolds number which can be carried out to large orders, and then extended analytically (thanks to a meromorphy property) beyond the disk of convergence. Secondly, there is a spectral method. The two methods typically agree within a fraction of 1%.A simple example, the ‘decorated hexagonal flow’, of a time-independent flow with isotropic negative eddy viscosity is given. Flows with randomly chosen Fourier components and the required symmetry have typically a 30% chance of developing a negative eddy viscosity when the Reynolds number is increased.For basic flow driven by a prescribed external force and sufficiently strong largescale flow, the analysis is extended to the nonlinear régime. It is found that the largescale dynamics is governed by a Navier-Stokes or a Navier-Stokes-Kuramoto-Sivashinsky equation, depending on the sign and strength of the eddy viscosity. When the driving force is not mirror-symmetric, a new ‘chiral’ nonlinearity appears. In special cases, the large-scale equation reduces to the Burgers equation. With chiral forcing, circular vortex patches are strongly enhanced or attenuated, depending on their cyclonicity.

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19

Weathers, J. B., and Rogelio Luck. "Time-Varying Uncertainty in Shock and Vibration Applications Using the Impulse Response." Shock and Vibration 19, no. 3 (2012): 433–46. http://dx.doi.org/10.1155/2012/139309.

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Design of mechanical systems often necessitates the use of dynamic simulations to calculate the displacements (and their derivatives) of the bodies in a system as a function of time in response to dynamic inputs. These types of simulations are especially prevalent in the shock and vibration community where simulations associated with models having complex inputs are routine. If the forcing functions as well as the parameters used in these simulations are subject to uncertainties, then these uncertainties will propagate through the models resulting in uncertainties in the outputs of interest. The uncertainty analysis procedure for these kinds of time-varying problems can be challenging, and in many instances, explicit data reduction equations (DRE's), i.e., analytical formulas, are not available because the outputs of interest are obtained from complex simulation software, e.g. FEA programs. Moreover, uncertainty propagation in systems modeled using nonlinear differential equations can prove to be difficult to analyze. However, if (1) the uncertainties propagate through the models in a linear manner, obeying the principle of superposition, then the complexity of the problem can be significantly simplified. If in addition, (2) the uncertainty in the model parameters do not change during the simulation and the manner in which the outputs of interest respond to small perturbations in the external input forces is not dependent on when the perturbations are applied, then the number of calculations required can be greatly reduced. Conditions (1) and (2) characterize a Linear Time Invariant (LTI) uncertainty model. This paper seeks to explain one possible approach to obtain the uncertainty results based on these assumptions.

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Sukhinin, B. V., and V. V. Surkov. "Analytical Construction Robust Optimal Control Systems by the Criterion of Quick Action with Inﬁnitely High Gain." Mekhatronika, Avtomatizatsiya, Upravlenie 21, no. 8 (August 5, 2020): 453–63. http://dx.doi.org/10.17587/mau.21.453-463.

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The problem of the synthesis of robust control systems with a high gain and, in particular, optimal by the criterion of quick action, which allow optimal control by the accuracy of regulation of multidimensional non-linear dynamic objects with functional uncertainties, is discussed. A method is proposed for the analytical construction of optimal control systems by the criterion of quick action for a wide class of multidimensional nonlinear dynamic objects with functional uncertainties, unstable objects; no minimal-phase objects, neutral object and objects with differentiation properties. Simplicity and universality, mathematical rigor and physical validity of this method consists in usingR.R Be llman’s method and decomposing the optimal by the criterion of quick action problem into a series of simple first-order simple problems of the same type. A theoretically comprehensive solution to the robust control problem is given by the idea of constructing systems that are stable with an unlimited increase in gain. In this case, optimal systems have stability properties. Such systems are synthesized using quadratic quality functionals that are not explicitly dependent on the control signal and the restriction on the control signal. It is significant that, in contrast to continuous systems with unmeasurable perturbations and a little-known object, in which the conditions of invariance require the use of infinitely large gains, in relay (discontinuous) systems, the equivalent effect is achieved using finite control actions. Since the performance problem is a particular problem of the accuracy of reproducing the input action on the control object, the established control error (including all error coefficients: by position, speed, acceleration, jerk, etc.) is theoretically strictly equal to zero if external and internal interference, acting only on the control object, but not on the control system, including sensors of state variables of the control object or the input signal of the task. However, due to the inertia of the object, there can be no talk of accuracy in the transient process of working out the input signal of the task, even if it is optimal in terms of the criterion of fast action.

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Bastrukov, S. I., J. Libert, and I. V. Molodtsova. "Elastodynamic Features of Nuclear Matter from Macroscopic Model of Giant Magnetic Resonances." International Journal of Modern Physics E 06, no. 01 (March 1997): 89–110. http://dx.doi.org/10.1142/s0218301397000068.

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The collective model is presented providing a descriptive treatment of the magnetic resonant response of spherical nuclei. The model is based on macroscopic equations assuming elastodynamic behavior of the nuclear Fermi-continuum. Modelling a heavy nucleus by a spherical piece of an elastic continuous substance made up of a degenerate Fermi-system of nucleons, it is argued that nuclear resonant magnetization may be interpreted as the resultant of torsional wavelike vibrations excited inside a nuclear macroparticle. The emphasis is placed on the description of the giant magnetic dipole resonance. This resonance is associated with long wavelength vibrations of the magnetization current induced in the peripheral layer of finite depth, whereas the internal spherical region presumably unaffected by external perturbations is considered as an unperturbed core. The excited collective motion is found to behave like shear non-radial vibrations of a massive peripheral layer against a rotationally invariant core. The Extended Thomas-Fermi method is employed to generate a bulk density profile on the basis of Skyrme forces which is used as an input parameter in calculations of torsional inertia and stiffness of the collective Hamiltonian. Systematic calculations for the energy and total excitation probability of the giant M1 resonance are compared with data obtained both by nuclear resonance fluorescence measurements and by means of backward (e,e′) scattering.

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22

Colonius, F., and W. Kliemann. "Invariance Under Bounded Time-Varying Perturbations." IFAC Proceedings Volumes 33, no. 16 (July 2000): 433–36. http://dx.doi.org/10.1016/s1474-6670(17)39670-2.

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23

Kochetkov, S. A., and V. A. Utkin. "Invariance in systems with unmatched perturbations." Automation and Remote Control 74, no. 7 (July 2013): 1097–127. http://dx.doi.org/10.1134/s0005117913070047.

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24

Liu, Yan. "Invariance of Deficiency Indices of Second-Order Symmetric Linear Difference Equations under Perturbations." Journal of Function Spaces 2020 (February 13, 2020): 1–6. http://dx.doi.org/10.1155/2020/1940481.

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This paper focuses on the invariance of deficiency indices of second-order symmetric linear difference equations under perturbations. By applying the perturbation theory of Hermitian linear relations, the invariance of deficiency indices of the corresponding minimal subspaces under bounded and relatively bounded perturbations is built. As a consequence, the invariance of limit types of second-order symmetric linear difference equations under bounded and relatively bounded perturbations is obtained.

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Biferale, L., K. Gustavsson, and R. Scatamacchia. "Helicoidal particles in turbulent flows with multi-scale helical injection." Journal of Fluid Mechanics 869 (May 2, 2019): 646–73. http://dx.doi.org/10.1017/jfm.2019.237.

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We present numerical and theoretical results concerning the properties of turbulent flows with strong multi-scale helical injection. We perform direct numerical simulations of the Navier–Stokes equations under a random helical stirring with power-law spectrum and with different intensities of energy and helicity injections. We show that there exists three different regimes where the forward energy and helicity inertial transfers are: (i) both leading with respect to the external injections, (ii) energy transfer is leading and helicity transfer is sub-leading and (iii) both are sub-leading and helicity is maximal at all scales. As a result, the cases (ii)–(iii) give flows with Kolmogorov-like inertial energy cascade and tuneable helicity transfers/contents. We further explore regime (iii) by studying its effect on the kinetics of point-like isotropic helicoids, particles whose dynamics is isotropic but breaks parity invariance. We investigate small-scale fractal clustering and preferential sampling of intense helical flow structures. Depending on their structural parameters, the isotropic helicoids either preferentially sample co-chiral or anti-chiral flow structures. We explain these findings in limiting cases in terms of what is known for spherical particles of different densities and degrees of inertia. Furthermore, we present theoretical and numerical results for a stochastic model where dynamical properties can be calculated using analytical perturbation theory. Our study shows that a suitable tuning of the stirring mechanism can strongly modify the small-scale turbulent helical properties and demonstrates that isotropic helicoids are the simplest particles able to preferentially sense helical properties in turbulence.

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CHIMENTO, LUIS P., and WINFRIED ZIMDAHL. "DUALITY INVARIANCE AND COSMOLOGICAL DYNAMICS." International Journal of Modern Physics D 17, no. 12 (November 2008): 2229–54. http://dx.doi.org/10.1142/s0218271808013820.

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A duality transformation that interrelates expanding and contracting cosmological models is shown to single out a duality invariant, interacting two-component description of any irrotational, geodesic and shear-free cosmic medium with vanishing three-curvature scalar. We have applied this feature to a system of matter and radiation, to a mixture of dark matter and dark energy, to minimal and conformal scalar fields, and to an enlarged Chaplygin gas model of the cosmic substratum. We have extended the concept of duality transformations to cosmological perturbations and demonstrated the invariance of adiabatic pressure perturbations under these transformations.

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27

Artstein, Zvi. "Invariance principle in the singular perturbations limit." Discrete & Continuous Dynamical Systems - B 24, no. 8 (2019): 3653–66. http://dx.doi.org/10.3934/dcdsb.2018309.

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28

Jung, K. "Adiabatic invariance and the regularity of perturbations." Nonlinearity 8, no. 6 (November 1, 1995): 891–900. http://dx.doi.org/10.1088/0951-7715/8/6/001.

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Nakai, Mitsuru, and Toshimasa Tada. "Invariance of Picard Dimensions Under Basic Perturbations." Potential Analysis 27, no. 3 (July 19, 2007): 199–215. http://dx.doi.org/10.1007/s11118-007-9057-1.

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30

Lucarini, V., and S. Sarno. "A statistical mechanical approach for the computation of the climatic response to general forcings." Nonlinear Processes in Geophysics 18, no. 1 (January 12, 2011): 7–28. http://dx.doi.org/10.5194/npg-18-7-2011.

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Abstract. The climate belongs to the class of non-equilibrium forced and dissipative systems, for which most results of quasi-equilibrium statistical mechanics, including the fluctuation-dissipation theorem, do not apply. In this paper we show for the first time how the Ruelle linear response theory, developed for studying rigorously the impact of perturbations on general observables of non-equilibrium statistical mechanical systems, can be applied with great success to analyze the climatic response to general forcings. The crucial value of the Ruelle theory lies in the fact that it allows to compute the response of the system in terms of expectation values of explicit and computable functions of the phase space averaged over the invariant measure of the unperturbed state. We choose as test bed a classical version of the Lorenz 96 model, which, in spite of its simplicity, has a well-recognized prototypical value as it is a spatially extended one-dimensional model and presents the basic ingredients, such as dissipation, advection and the presence of an external forcing, of the actual atmosphere. We recapitulate the main aspects of the general response theory and propose some new general results. We then analyze the frequency dependence of the response of both local and global observables to perturbations having localized as well as global spatial patterns. We derive analytically several properties of the corresponding susceptibilities, such as asymptotic behavior, validity of Kramers-Kronig relations, and sum rules, whose main ingredient is the causality principle. We show that all the coefficients of the leading asymptotic expansions as well as the integral constraints can be written as linear function of parameters that describe the unperturbed properties of the system, such as its average energy. Some newly obtained empirical closure equations for such parameters allow to define such properties as an explicit function of the unperturbed forcing parameter alone for a general class of chaotic Lorenz 96 models. We then verify the theoretical predictions from the outputs of the simulations up to a high degree of precision. The theory is used to explain differences in the response of local and global observables, to define the intensive properties of the system, which do not depend on the spatial resolution of the Lorenz 96 model, and to generalize the concept of climate sensitivity to all time scales. We also show how to reconstruct the linear Green function, which maps perturbations of general time patterns into changes in the expectation value of the considered observable for finite as well as infinite time. Finally, we propose a simple yet general methodology to study general Climate Change problems on virtually any time scale by resorting to only well selected simulations, and by taking full advantage of ensemble methods. The specific case of globally averaged surface temperature response to a general pattern of change of the CO2 concentration is discussed. We believe that the proposed approach may constitute a mathematically rigorous and practically very effective way to approach the problem of climate sensitivity, climate prediction, and climate change from a radically new perspective.

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31

Solnechnyi, E. M. "Invariance and astatism in systems not measuring perturbations." Automation and Remote Control 69, no. 12 (December 2008): 2061–69. http://dx.doi.org/10.1134/s0005117908120059.

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32

Watanabe, Yuki, Atsushi Naruko, and Misao Sasaki. "Multi-disformal invariance of non-linear primordial perturbations." EPL (Europhysics Letters) 111, no. 3 (August 1, 2015): 39002. http://dx.doi.org/10.1209/0295-5075/111/39002.

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33

Seidman, Thomas I. "Invariance of the Reachable Set under Nonlinear Perturbations." SIAM Journal on Control and Optimization 25, no. 5 (September 1987): 1173–91. http://dx.doi.org/10.1137/0325064.

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34

Gouda, Ya. "Homotopy invariance of perturbations of D ∞-differential modules." Mathematical Notes 96, no. 3-4 (September 2014): 353–59. http://dx.doi.org/10.1134/s0001434614090077.

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35

Klapp, Sabine H. L. "Dipolar fluids under external perturbations." Journal of Physics: Condensed Matter 17, no. 15 (April 2, 2005): R525—R550. http://dx.doi.org/10.1088/0953-8984/17/15/r02.

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36

Naito, Koichiro, and Thomas I. Seidman. "Invariance of the Approximately Reachable Set under Nonlinear Perturbations." SIAM Journal on Control and Optimization 29, no. 3 (May 1991): 731–50. http://dx.doi.org/10.1137/0329040.

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37

SOH, C. B. "Invariance of strict aperiodicity for systems with dependent perturbations." International Journal of Systems Science 25, no. 11 (November 1994): 1931–39. http://dx.doi.org/10.1080/00207729408949323.

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38

Zubova, S. P., and E. B. Raetskaya. "Invariance of a nonstationary observability system under certain perturbations." Journal of Mathematical Sciences 188, no. 3 (December 15, 2012): 218–26. http://dx.doi.org/10.1007/s10958-012-1120-9.

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39

Chang, Zhe, Sai Wang, and Qing-Hua Zhu. "Note on gauge invariance of second order cosmological perturbations *." Chinese Physics C 45, no. 9 (September 1, 2021): 095101. http://dx.doi.org/10.1088/1674-1137/ac0c74.

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40

Kulakou, G. Т., and A. Т. Kulakou. "Basic principles of construction of high-quality analytical adaptable control systems for thermal energy processes." Doklady BGUIR 19, no. 6 (October 1, 2021): 97–101. http://dx.doi.org/10.35596/1729-7648-2021-19-6-97-102.

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The modeling results and industrial tests of a typical automatic control system (ACS) and the proposed invariant cascade ACS are presented. The advantages of structural-parametric optimization methods for creating high-quality control systems for heat-and-power processes have been substantiated. The following algorithm for forming a block diagram of a high-quality invariant cascade SAR is proposed. At the beginning, the structure of the optimal transfer function of the stabilizing regulator is determined as the product of the inverse transfer function of the leading section of the object by a given transfer function of the open system of the internal circuit in the form of an ideal integrating link with one calculated parameter of dynamic tuning, which allows optimally working out both internal disturbances and the task of the stabilizing regulator. Then, the parameters of the dynamic adjustment of the corrective regulator are calculated for optimal processing of the extreme external disturbance. Next, an equivalent external perturbation is isolated without its direct measurement using a complete model of the inertial section of the object. At the same time, the obtained difference between the main adjustable value and the model output is fed to the input of an equivalent external perturbation compensation device implemented in the form of a differentiator, which makes it possible to increase the accuracy and speed of the invariant SAR compared to the standard one. To ensure high quality control over the entire range of load changes, the parameters of the dynamic adjustment of the invariant SAR and the model of the inertial section are adjusted in the load function.

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41

Roques, Lionel, and Mickaël D. Chekroun. "On Population Resilience to External Perturbations." SIAM Journal on Applied Mathematics 68, no. 1 (January 2007): 133–53. http://dx.doi.org/10.1137/060676994.

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42

Bruni, Marco, Leonardo Gualtieri, and Carlos F. Sopuerta. "Two-parameter nonlinear spacetime perturbations: gauge transformations and gauge invariance." Classical and Quantum Gravity 20, no. 3 (January 16, 2003): 535–56. http://dx.doi.org/10.1088/0264-9381/20/3/310.

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43

Langlois, David. "Hamiltonian formalism and gauge invariance for linear perturbations in inflation." Classical and Quantum Gravity 11, no. 2 (February 1, 1994): 389–407. http://dx.doi.org/10.1088/0264-9381/11/2/011.

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44

Srinivas, V., and Vijayalaxmi Trivedi. "The Invariance of Hilbert Functions of Quotients under Small Perturbations." Journal of Algebra 186, no. 1 (November 1996): 1–19. http://dx.doi.org/10.1006/s0021-8693(96)90000-9.

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45

Frank, Steven A. "Invariant death." F1000Research 5 (August 25, 2016): 2076. http://dx.doi.org/10.12688/f1000research.9456.1.

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In nematodes, environmental or physiological perturbations alter death’s scaling of time. In human cancer, genetic perturbations alter death’s curvature of time. Those changes in scale and curvature follow the constraining contours of death’s invariant geometry. I show that the constraints arise from a fundamental extension to the theories of randomness, invariance and scale. A generalized Gompertz law follows. The constraints imposed by the invariant Gompertz geometry explain the tendency of perturbations to stretch or bend death’s scaling of time. Variability in death rate arises from a combination of constraining universal laws and particular biological processes.

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46

LU, YAO, and YUN-SONG PIAO. "SCALE INVARIANCE FROM MODIFIED DISPERSION RELATIONS." International Journal of Modern Physics D 19, no. 12 (October 2010): 1905–14. http://dx.doi.org/10.1142/s0218271810018074.

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In this paper, inspired by the investigations on the theory of cosmological perturbations in Hořava–Lifshitz cosmology, we calculate the spectrum of primordial perturbation lead by a modified dispersion relation in proper time ω pro ~ kz/ap in power-law expansion/contraction background a ~ tn · z is the critical exponent and p is not necessarily equal to z · p = z is well-motivated by Hořava–Lifshitz gravity, and the cases with p ≠ z are generalizations beyond the scope. We discuss that for fixed z, if the spectrum is required to be scale-invariant, how should p depend on n. We conclude that there is always room for parameters for the generation of scale-invariant spectrum.

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47

Stoica, Sabin. "Tests of the Lorentz invariance violation in double-beta decay." Journal of Physics: Conference Series 2156, no. 1 (December 1, 2021): 012152. http://dx.doi.org/10.1088/1742-6596/2156/1/012152.

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Abstract Testing the Lorentz invariance violation (LIV) double-beta decay (DBD) is an interesting, recently opened topic, currently under investigation. Theoretically, LIV can be induced in this process by coupling neutrinos to the countershaded operator in the Standard Model extension (SME) theory, particularly to its time-like component, and could manifest as small perturbations in the shape of the energy spectra of electrons. In the absence of observation of such perturbations, one can constrain the values of the oscillation-free (of) coefficient å o f ( 3 ) , that controlled the size of the LIV effects. Such investigations are currently been conducted in several DBD experiments and are based on theoretical predictions of the electron spectra and angular correlation between electrons in 2νββ decay. In this paper I first present some general considerations about DBD and then give a brief review of the current status of LIV searches in the study of this process.

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48

Bruni, Marco, and Sebastiano Sonego. "Observables and gauge invariance in the theory of nonlinear spacetime perturbations." Classical and Quantum Gravity 16, no. 7 (January 1, 1999): L29—L36. http://dx.doi.org/10.1088/0264-9381/16/7/101.

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49

Br�ning, E., M. Demuth, and F. Gesztesy. "Invariance of the essential spectra for perturbations with unbounded hard cores." Letters in Mathematical Physics 13, no. 1 (January 1987): 69–77. http://dx.doi.org/10.1007/bf00570770.

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50

Maistrenko, Yu L. "Invariance of noncompact iterated sequences under perturbations of certain nonlinear operators." Ukrainian Mathematical Journal 41, no. 7 (July 1989): 779–84. http://dx.doi.org/10.1007/bf01060692.

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